Axial-Current Anomaly in Euler Fluid

TL;DR

This paper demonstrates that an axial-current anomaly similar to that in quantum field theories also occurs in classical Euler fluids, linking electromagnetic fields to helicity conservation breaking.

Contribution

It reveals a novel classical analog of the quantum axial-current anomaly within the framework of Euler fluid dynamics.

Findings

Axial current conservation in Euler fluids is broken by electromagnetic fields.

The anomaly relation in Euler fluids mirrors that of quantum field theories like QED.

Helicity conservation is anomalously broken by external electromagnetic influences.

Abstract

We argue that a close analog of the axial-current anomaly of quantum field theories with fermions occurs in the classical Euler fluid. The conservation of the axial current (closely related to the helicity of inviscid barotropic flow) is anomalously broken by the external electromagnetic field as $\partial_\mu j_{A}^\mu = 2\,\bf E\!\cdot\! \bf B$ similar to that of the axial current of a quantum field theory with Dirac fermions such as QED.